We don't understand yet, in any formal sense, what consciousness and subjective experience are. It may turn out that they are fundamentally different than mathematics and computation, but the vast majority of scientists believe today that they are not.

The most common belief is that consciousness is simply the self-introspection of a sufficiently powerful computer that can form models of other agents. That is, this computer is able to infer what other agents may do using a model of their inner state, such as beliefs about the world and desires; then, if it applies the same model to itself, it comes up with a similar image of an agent which it calls its own consciousness. Qualia and such are then just illusions, theoretical properties of these models, not fundemantal properties of this world (somewhat equivalent to saying that in fact we are all philosophical zombies, no one has any qualia).

I am not claiming that we know for a fact this is true. But we also don't know anything that can conclusively disprove these hypotheses for now, certainly not something as simple as the idea of qualia.